On the Integrability of Non-Polynomial Scalar Evolution Equations

Sanders, Jan A. and Wang, Jing Ping (2000) On the Integrability of Non-Polynomial Scalar Evolution Equations. Journal of Differential Equations, 166 (1). pp. 132-150. ISSN 0022-0396. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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We show the existence of infinitely many symmetries for λ-homogeneous equations when λ=0. If the equation has one generalized symmetry, we prove that it has infinitely many and these can be produced by recursion operators. Identifying equations under homogeneous transformations, we find that the only integrable equations in this class are the Potential Burgers, Potential Modified Korteweg–de Vries, and Potential Kupershmidt Equations. We can draw some conclusions from these results for the case λ=−1 which, although theoretically incomplete, seem to cover the known integrable systems for this case.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Jing Ping Wang
Date Deposited: 26 May 2009 20:00
Last Modified: 11 Jun 2014 09:07
Resource URI: https://kar.kent.ac.uk/id/eprint/8833 (The current URI for this page, for reference purposes)
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